cp's OEIS Frontend

A302040 Numbers k such that A078898(k) is a power of 2; an analog for A000961 based on factorization-kind of process involving the sieve of Eratosthenes (A083221).

%I A302040 #22 Jul 21 2021 00:44:54
%S A302040 1,2,3,4,5,7,8,9,11,13,16,17,19,21,23,25,29,31,32,37,41,43,45,47,49,
%T A302040 53,55,59,61,64,67,71,73,79,83,89,91,93,97,101,103,107,109,113,115,
%U A302040 121,127,128,131,137,139,149,151,157,163,167,169,173,179,181,187,189,191,193,197,199,203,211,223,227,229,233,235,239,241,247,251,256,257
%N A302040 Numbers k such that A078898(k) is a power of 2; an analog for A000961 based on factorization-kind of process involving the sieve of Eratosthenes (A083221).
%C A302040 Numbers k for which A302041(k) < 2, or equally, for which A302044(k) = 1.
%C A302040 Sequence A250245(A000961(k)) sorted into ascending order, or in other words, numbers k such that A250246(k) is a prime power (in A000961).
%C A302040 Numbers k such that all terms in iteration sequence k, A302042(k), A302042(A302042(k)), A302042(A302042(A302042(k))), ..., have an equal smallest prime factor (A020639) before the sequence settles to 1, in other words, that they all stay on the same row of A083221. This also forces the column position of each (A078898) to be a power of 2 (A000079).
%H A302040 Antti Karttunen, <a href="/A302040/b302040.txt">Table of n, a(n) for n = 1..6883</a>
%H A302040 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%e A302040 For k = 21 = 3*7, the smallest prime factor is 3. A302042(21) = 9, and A302042(9) = 3, both (9 and 3) which also have 3 as their smallest prime factor, and after that the sequence settles to 1, as A302042(3) = 1, thus 21 is included in this sequence.
%e A302040 For k = 27 = 3*3*3, the smallest prime factor is 3. However, A302042(27) = 7, thus 27 is not included in this sequence.
%o A302040 (PARI) for(n=1,257,if(2>A302041(n),print1(n,","))); \\ Other code as in A302041.
%Y A302040 Cf. A000961, A078898, A302036, A302041, A302044, A302053.
%Y A302040 Cf. A000040, A000079, A001248 (subsequences).
%K A302040 nonn
%O A302040 1,2
%A A302040 _Antti Karttunen_, Apr 02 2018